Testing the effect of deviance on similarity-based structure and certainty.
Hypothesis: We predict that as a new agent’s deviance from the group stereotype increases there will be a transition from group updating to subgroup formation to subtype formation. This will be reflected in participants’ similarity-rating derived dendrograms.
Method: 8 agents, 8 issues
| 0 (N=52) |
0.25 (N=72) |
0.5 (N=60) |
0.75 (N=49) |
1 (N=51) |
Overall (N=284) |
|
|---|---|---|---|---|---|---|
| age | ||||||
| Mean (SD) | 35.4 (13.7) | 36.1 (12.7) | 33.9 (12.2) | 37.7 (13.7) | 36.9 (10.7) | 35.9 (12.6) |
| Median [Min, Max] | 32.0 [18.0, 72.0] | 34.0 [18.0, 75.0] | 33.0 [18.0, 71.0] | 36.0 [20.0, 71.0] | 35.0 [20.0, 62.0] | 34.0 [18.0, 75.0] |
| race | ||||||
| American Indian or Alaska Native | 1 (1.9%) | 1 (1.4%) | 2 (3.3%) | 1 (2.0%) | 0 (0%) | 5 (1.8%) |
| Asian | 6 (11.5%) | 6 (8.3%) | 8 (13.3%) | 3 (6.1%) | 6 (11.8%) | 29 (10.2%) |
| Black or African-American | 5 (9.6%) | 5 (6.9%) | 4 (6.7%) | 6 (12.2%) | 1 (2.0%) | 21 (7.4%) |
| Hispanic/Latinx | 3 (5.8%) | 5 (6.9%) | 5 (8.3%) | 2 (4.1%) | 1 (2.0%) | 16 (5.6%) |
| White | 37 (71.2%) | 53 (73.6%) | 41 (68.3%) | 37 (75.5%) | 41 (80.4%) | 209 (73.6%) |
| Native Hawaiian or Other Pacific Islander | 0 (0%) | 1 (1.4%) | 0 (0%) | 0 (0%) | 0 (0%) | 1 (0.4%) |
| Other | 0 (0%) | 1 (1.4%) | 0 (0%) | 0 (0%) | 2 (3.9%) | 3 (1.1%) |
| gender | ||||||
| Man | 20 (38.5%) | 23 (31.9%) | 19 (31.7%) | 18 (36.7%) | 24 (47.1%) | 104 (36.6%) |
| Woman | 32 (61.5%) | 46 (63.9%) | 40 (66.7%) | 29 (59.2%) | 23 (45.1%) | 170 (59.9%) |
| Non-binary | 0 (0%) | 2 (2.8%) | 1 (1.7%) | 1 (2.0%) | 2 (3.9%) | 6 (2.1%) |
| Prefer not to answer | 0 (0%) | 1 (1.4%) | 0 (0%) | 1 (2.0%) | 2 (3.9%) | 4 (1.4%) |
| 0 (N=4) |
0.25 (N=6) |
0.5 (N=2) |
0.75 (N=2) |
1 (N=3) |
Overall (N=17) |
|
|---|---|---|---|---|---|---|
| age | ||||||
| Mean (SD) | 35.3 (9.46) | 39.0 (21.8) | 35.5 (4.95) | 51.5 (21.9) | 44.7 (26.3) | 40.2 (17.7) |
| Median [Min, Max] | 31.5 [29.0, 49.0] | 29.5 [24.0, 82.0] | 35.5 [32.0, 39.0] | 51.5 [36.0, 67.0] | 40.0 [21.0, 73.0] | 34.0 [21.0, 82.0] |
| race | ||||||
| White | 4 (100%) | 5 (83.3%) | 1 (50.0%) | 2 (100%) | 2 (66.7%) | 14 (82.4%) |
| Asian | 0 (0%) | 1 (16.7%) | 0 (0%) | 0 (0%) | 0 (0%) | 1 (5.9%) |
| Black or African-American | 0 (0%) | 0 (0%) | 1 (50.0%) | 0 (0%) | 1 (33.3%) | 2 (11.8%) |
| gender | ||||||
| Man | 1 (25.0%) | 1 (16.7%) | 1 (50.0%) | 1 (50.0%) | 1 (33.3%) | 5 (29.4%) |
| Woman | 3 (75.0%) | 4 (66.7%) | 1 (50.0%) | 1 (50.0%) | 2 (66.7%) | 11 (64.7%) |
| Another gender not listed here | 0 (0%) | 1 (16.7%) | 0 (0%) | 0 (0%) | 0 (0%) | 1 (5.9%) |
Analysis of Deviance Table (Type II Wald chisquare tests)
Response: corrresp
Chisq Df Pr(>Chisq)
opinion_round 155.5722 1 < 2.2e-16 ***
Deviant_threshold 29.9063 4 5.114e-06 ***
opinion_round:Deviant_threshold 1.8352 4 0.766
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 1 opinion_round.trend SE df asymp.LCL asymp.UCL z.ratio p.value
overall 0.186 0.0152 Inf 0.157 0.216 12.282 <.0001
Results are averaged over the levels of: Deviant_threshold
Confidence level used: 0.95 $emmeans
Deviant_threshold emmean SE df asymp.LCL asymp.UCL z.ratio p.value
0 1.59 0.1099 Inf 1.374 1.80 14.461 <.0001
0.25 1.04 0.0906 Inf 0.864 1.22 11.494 <.0001
0.5 1.01 0.0993 Inf 0.813 1.20 10.147 <.0001
0.75 1.02 0.1099 Inf 0.807 1.24 9.303 <.0001
1 1.15 0.1080 Inf 0.943 1.37 10.692 <.0001
Results are given on the logit (not the response) scale.
Confidence level used: 0.95
$contrasts
contrast estimate SE df asymp.LCL
Deviant_threshold0 - Deviant_threshold0.25 0.5479 0.142 Inf 0.1611
Deviant_threshold0 - Deviant_threshold0.5 0.5816 0.147 Inf 0.1795
Deviant_threshold0 - Deviant_threshold0.75 0.5663 0.155 Inf 0.1440
Deviant_threshold0 - Deviant_threshold1 0.4345 0.153 Inf 0.0161
Deviant_threshold0.25 - Deviant_threshold0.5 0.0337 0.134 Inf -0.3314
Deviant_threshold0.25 - Deviant_threshold0.75 0.0185 0.142 Inf -0.3688
Deviant_threshold0.25 - Deviant_threshold1 -0.1134 0.140 Inf -0.4964
Deviant_threshold0.5 - Deviant_threshold0.75 -0.0153 0.148 Inf -0.4180
Deviant_threshold0.5 - Deviant_threshold1 -0.1471 0.146 Inf -0.5457
Deviant_threshold0.75 - Deviant_threshold1 -0.1318 0.154 Inf -0.5508
asymp.UCL z.ratio p.value
0.935 3.864 0.0011
0.984 3.945 0.0008
0.989 3.658 0.0024
0.853 2.832 0.0373
0.399 0.252 0.9991
0.406 0.130 0.9999
0.270 -0.807 0.9284
0.387 -0.103 1.0000
0.252 -1.007 0.8525
0.287 -0.858 0.9120
Results are given on the log odds ratio (not the response) scale.
Confidence level used: 0.95
Conf-level adjustment: tukey method for comparing a family of 5 estimates
P value adjustment: tukey method for comparing a family of 5 estimates Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
targetpair 334 334 1 284 1.6629 0.1983
Deviant_threshold 33776 33776 1 284 168.2303 <2e-16 ***
targetpair:Deviant_threshold 45254 45254 1 284 225.3989 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1$emtrends
targetpair Deviant_threshold.trend SE df lower.CL upper.CL t.ratio p.value
DN -62.2667 3.45 284 -69.05 -55.48 -18.057 <.0001
NN 0.0141 2.87 284 -5.63 5.66 0.005 0.9961
Degrees-of-freedom method: satterthwaite
Confidence level used: 0.95
$contrasts
contrast estimate SE df lower.CL upper.CL t.ratio p.value
DN - NN -62.3 4.15 284 -70.4 -54.1 -15.013 <.0001
Degrees-of-freedom method: satterthwaite
Confidence level used: 0.95 Analysis of Variance Table
Response: k
Df Sum Sq Mean Sq F value Pr(>F)
Deviant_threshold 4 23.943 5.9857 16.327 4.967e-12 ***
Residuals 279 102.283 0.3666
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1$emmeans
Deviant_threshold emmean SE df lower.CL upper.CL t.ratio p.value
0 1.61 0.0840 279 1.44 1.78 19.178 <.0001
0.25 1.66 0.0714 279 1.51 1.80 23.198 <.0001
0.5 1.87 0.0782 279 1.72 2.02 23.930 <.0001
0.75 2.12 0.0865 279 1.95 2.29 24.471 <.0001
1 2.40 0.0848 279 2.24 2.57 28.348 <.0001
Confidence level used: 0.95
$contrasts
contrast estimate SE df lower.CL
Deviant_threshold0 - Deviant_threshold0.25 -0.0451 0.110 279 -0.348
Deviant_threshold0 - Deviant_threshold0.5 -0.2603 0.115 279 -0.575
Deviant_threshold0 - Deviant_threshold0.75 -0.5064 0.121 279 -0.837
Deviant_threshold0 - Deviant_threshold1 -0.7932 0.119 279 -1.121
Deviant_threshold0.25 - Deviant_threshold0.5 -0.2152 0.106 279 -0.506
Deviant_threshold0.25 - Deviant_threshold0.75 -0.4613 0.112 279 -0.769
Deviant_threshold0.25 - Deviant_threshold1 -0.7481 0.111 279 -1.052
Deviant_threshold0.5 - Deviant_threshold0.75 -0.2461 0.117 279 -0.566
Deviant_threshold0.5 - Deviant_threshold1 -0.5329 0.115 279 -0.850
Deviant_threshold0.75 - Deviant_threshold1 -0.2868 0.121 279 -0.619
upper.CL t.ratio p.value
0.2575 -0.409 0.9941
0.0547 -2.269 0.1581
-0.1754 -4.201 0.0003
-0.4656 -6.647 <.0001
0.0754 -2.033 0.2528
-0.1534 -4.114 0.0005
-0.4439 -6.751 <.0001
0.0740 -2.111 0.2183
-0.2163 -4.621 0.0001
0.0458 -2.368 0.1273
Confidence level used: 0.95
Conf-level adjustment: tukey method for comparing a family of 5 estimates
P value adjustment: tukey method for comparing a family of 5 estimates Deviant_threshold emmean SE df null t.ratio p.value
0 1.61 0.0840 279 2 -4.642 <.0001
0.25 1.66 0.0714 279 2 -4.830 <.0001
0.5 1.87 0.0782 279 2 -1.656 0.0494
0.75 2.12 0.0865 279 2 1.349 0.9108
1 2.40 0.0848 279 2 4.759 1.0000
P values are left-tailed # A tibble: 2 × 8
model term estimate std.error statistic p.value conf.low conf.high
<chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 below_.5 Deviant_thre… -14.2 9.80 -1.45 0.149 -33.5 5.15
2 above_.5 Deviant_thre… -14.3 10.6 -1.35 0.178 -35.2 6.59Analysis of Variance Table
Response: confidence
Df Sum Sq Mean Sq F value Pr(>F)
deviance 4 6957 1739.34 2.4753 0.04459 *
Residuals 279 196044 702.67
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1$emmeans
deviance emmean SE df lower.CL upper.CL t.ratio p.value
0 60.3 3.68 279 53.1 67.6 16.411 <.0001
0.25 56.1 3.12 279 50.0 62.3 17.961 <.0001
0.5 53.2 3.42 279 46.5 59.9 15.546 <.0001
0.75 48.4 3.79 279 40.9 55.8 12.778 <.0001
1 46.1 3.71 279 38.8 53.4 12.419 <.0001
Confidence level used: 0.95
$contrasts
contrast estimate SE df lower.CL upper.CL t.ratio
deviance0 - deviance0.25 4.22 4.82 279 -9.030 17.5 0.874
deviance0 - deviance0.5 7.13 5.02 279 -6.663 20.9 1.419
deviance0 - deviance0.75 11.94 5.28 279 -2.552 26.4 2.262
deviance0 - deviance1 14.23 5.22 279 -0.115 28.6 2.724
deviance0.25 - deviance0.5 2.91 4.63 279 -9.811 15.6 0.628
deviance0.25 - deviance0.75 7.72 4.91 279 -5.756 21.2 1.573
deviance0.25 - deviance1 10.01 4.85 279 -3.308 23.3 2.064
deviance0.5 - deviance0.75 4.81 5.10 279 -9.202 18.8 0.943
deviance0.5 - deviance1 7.10 5.05 279 -6.760 21.0 1.407
deviance0.75 - deviance1 2.29 5.30 279 -12.270 16.8 0.432
p.value
0.9063
0.6159
0.1604
0.0530
0.9704
0.5158
0.2388
0.8799
0.6239
0.9927
Confidence level used: 0.95
Conf-level adjustment: tukey method for comparing a family of 5 estimates
P value adjustment: tukey method for comparing a family of 5 estimates | 0 (N=52) |
0.25 (N=72) |
0.5 (N=60) |
0.75 (N=49) |
1 (N=51) |
Overall (N=284) |
|
|---|---|---|---|---|---|---|
| pred_maj | ||||||
| Yes | 46 (88.5%) | 56 (77.8%) | 43 (71.7%) | 41 (83.7%) | 39 (76.5%) | 225 (79.2%) |
| No | 6 (11.5%) | 16 (22.2%) | 17 (28.3%) | 8 (16.3%) | 12 (23.5%) | 59 (20.8%) |
# A tibble: 4 × 9
# Groups: pred_maj [2]
pred_maj id term estimate std.error statistic p.value conf.low conf.high
<lgl> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 FALSE below_… Devi… -12.7 24.5 -0.519 0.607 -62.3 36.9
2 FALSE above_… Devi… -21.4 20.8 -1.03 0.312 -63.7 20.9
3 TRUE below_… Devi… -8.26 10.5 -0.789 0.432 -29.0 12.4
4 TRUE above_… Devi… -14.1 12.0 -1.18 0.242 -37.8 9.60Analysis of Variance Table
Response: confidence
Df Sum Sq Mean Sq F value Pr(>F)
deviance 4 6957 1739.3 2.5929 0.036928 *
pred_maj 1 10078 10077.5 15.0227 0.000133 ***
deviance:pred_maj 4 2162 540.5 0.8058 0.522346
Residuals 274 183805 670.8
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1| 0 (N=284) |
1 (N=284) |
2 (N=284) |
3 (N=284) |
4 (N=284) |
5 (N=284) |
6 (N=284) |
7 (N=284) |
Overall (N=2272) |
|
|---|---|---|---|---|---|---|---|---|---|
| trialnum | |||||||||
| 0 | 45 (15.8%) | 28 (9.9%) | 41 (14.4%) | 45 (15.8%) | 39 (13.7%) | 29 (10.2%) | 32 (11.3%) | 32 (11.3%) | 291 (12.8%) |
| 1 | 32 (11.3%) | 31 (10.9%) | 30 (10.6%) | 43 (15.1%) | 46 (16.2%) | 46 (16.2%) | 35 (12.3%) | 43 (15.1%) | 306 (13.5%) |
| 2 | 39 (13.7%) | 43 (15.1%) | 42 (14.8%) | 30 (10.6%) | 39 (13.7%) | 37 (13.0%) | 40 (14.1%) | 28 (9.9%) | 298 (13.1%) |
| 3 | 26 (9.2%) | 34 (12.0%) | 30 (10.6%) | 33 (11.6%) | 28 (9.9%) | 37 (13.0%) | 46 (16.2%) | 36 (12.7%) | 270 (11.9%) |
| 4 | 31 (10.9%) | 40 (14.1%) | 32 (11.3%) | 41 (14.4%) | 33 (11.6%) | 41 (14.4%) | 32 (11.3%) | 40 (14.1%) | 290 (12.8%) |
| 5 | 47 (16.5%) | 31 (10.9%) | 37 (13.0%) | 31 (10.9%) | 28 (9.9%) | 29 (10.2%) | 36 (12.7%) | 22 (7.7%) | 261 (11.5%) |
| 6 | 32 (11.3%) | 36 (12.7%) | 37 (13.0%) | 29 (10.2%) | 35 (12.3%) | 29 (10.2%) | 30 (10.6%) | 41 (14.4%) | 269 (11.8%) |
| 7 | 32 (11.3%) | 41 (14.4%) | 35 (12.3%) | 32 (11.3%) | 36 (12.7%) | 36 (12.7%) | 33 (11.6%) | 42 (14.8%) | 287 (12.6%) |
Possible interpretation of results:
Participants are demonstrating that they are learning about the deviant agent, but the degree of learning declines with subsequent tasks. This pattern could suggest that participant results reflect the first half of the structure learning model (up to the lowest point). Possible suggestion is to run 1B again with more chances to learn (ie more issues) to see if the results show an increase accuracy in learning about the deviant over a longer period of tasks.